We report on the precision determination of the top-quark mass to
next-to-next-to-leading order in QCD in well-defined renormalization schemes
using data from the Large Hadron Collider for single-top and top-quark pair
production. We also discuss the calibration of the so-called Monte Carlo
top-quark mass parameter which is determined from a comparison to events with
top-quark decay products. The implications of the measured value of the
top-quark mass for conclusions about the stability of the electroweak vacuum
state of our Universe are illustrated. At future lepton colliders, we provide
for the first time matched exclusive calculations valid both at the top
threshold and in the continuum, also fully differentially. In addition, we
calculate fully off-shell top-pair production (also with an associated Higgs
boson) at next-to-leading order in QCD, which allows to extract the top-Yukawa
coupling with an unprecedented precision.Comment: 15 pages, 8 figures. Part of the final report of the Collaborative
Research Center 676 "Particles, Strings and the Early Universe" 2006 - 201
